Probability and Compound Events: math test solutions, Grade 7 – download the PDF

1 Marbles / 3 pts

There are 10 marbles.

1. \( \dfrac{5}{10} = \dfrac{1}{2} \) (1 pt)
2. \( \dfrac{8}{10} = \dfrac{4}{5} \) (1 pt)
3. \( 0 \), the event is impossible (1 pt)

2 Experiment and prediction / 3 pts

1. \( \dfrac{30}{80} = \dfrac{3}{8} = 0.375 \) (1 pt)
2. \( \dfrac{1}{3} \approx 0.333 \) (1 pt)
3. \( \dfrac{22}{80} \times 400 = 110 \) reds (1 pt)

3 Two dice / 4 pts

1. (1,4), (2,3), (3,2), (4,1): \( \dfrac{4}{36} = \dfrac{1}{9} \) (1 pt)
2. Prime sums are 2, 3, 5, 7, 11 with \( 1 + 2 + 4 + 6 + 2 = 15 \) outcomes, so \( \dfrac{15}{36} = \dfrac{5}{12} \) (2 pts)
3. (1,1) to (6,6): \( \dfrac{6}{36} = \dfrac{1}{6} \) (1 pt)

4 Pizza orders / 4 pts

1. Thin-cheese, thin-pepperoni, thin-veggie, thick-cheese, thick-pepperoni, thick-veggie: 6 outcomes (1 pt)
2. \( \dfrac{1}{6} \) (1 pt)
3. 3 thin outcomes plus thick-pepperoni: \( \dfrac{4}{6} = \dfrac{2}{3} \) (1 pt)
4. \( \dfrac{1}{2} \times 120 = 60 \) thin crusts (1 pt)

5 A probability model / 3 pts

1. \( x = 1 - 0.4 - 0.15 - 0.1 = 0.35 \) (1 pt)
2. \( 0.35 + 0.15 = 0.5 \) (1 pt)
3. \( 0.1 \times 200 = 20 \) (1 pt)

6 Free-throw simulation / 3 pts

1. 40% of 10 digits is 4 digits, for example 0, 1, 2, 3 (1 pt)
2. The digits 2, 0, 3, 1, 2 are in the set, so \( \dfrac{5}{10} = 0.5 \) (1 pt)
3. Only 10 trials were made. A small number of trials can differ from the theoretical probability; more trials get closer to 0.4 (1 pt)